This invention relates to a method of determining the rate of change in frequency of random events and, more particularly, to such method when used to measure the rate of change of random neutron activity in nuclear reactors.
The frequency of a periodic signal is typically measured by counting the number of events (pulses, zero crossings, etc.) that have occurred over some fixed sample period, T. If C events are counted over this interval, the measured frequency of the signal, F, is simply calculated from the equation: EQU F=C/T
The rate of change in frequency can be calculated from two successive measurements of frequency F.sub.1 and F.sub.2 from the relationship: EQU Rate=(F.sub.2 -F.sub.1)/T
Graphically, the rate is depicted as the slope of a graph where a vertical axis, y-axis, is the number of events as a horizontal axis, x-axis, is the time. This equation works to calculate rate when the number of occurrences of the event is accurately known. But when the number of occurrences is varying statistically, inaccuracies result. For example, if an input from a source of random pulses has a Poisson distribution, the rate of change of mean frequency may be zero, but the observed rate of change may vary substantially for small numbers of counts per sample. The error in the measurement in slope can be reduced to an arbitrarily small value by increasing the length of the sample interval to a sufficiently large value or by averaging successive sample intervals to effectively increase the length of the sample interval. Thus it is apparent that averaging the inputs will produce a calculated rate that is much closer to the mean rate. This method works extremely well as long as a sufficient number of samples are used in the averages to offset the effects of randomness. At low levels of occurrences, this number is quite large and at high levels of occurrences, this number becomes substantially reduced. The exact number of readings needed to achieve a specified accuracy can be calculated using standard statistical methods. The response time of an instrument to the rate of change in the frequency of incoming pulses is directly related to the number of input samples used to calculate the pulse frequency. If N samples are used in this calculation, then the response time of the instrument will be between 2N and 2N+1 sample times. Therefore, accuracy and response time can be traded off in a straight forward manner.
Within a nuclear reactor, neutron activity is an indication of the power being generated by the reactor and an indication of the rate of change of neutron activity is important for both control and safety systems. With a very wide range of neutron activity, which may vary from a few pulses per second to millions of pulses per second, rather than measuring the linear rate of change of activity as described above, the measurement of exponential rate of change (typically in decades per minute) is more appropriate. The equation used for the exponential rate of change of neutron activity is given by EQU Rate=(log (F.sub.2)-log (F.sub.1))/T EQU or EQU Rate =(log (F.sub.2 /F.sub.1))/T
where F.sub.1 and F.sub.2 are two consecutive measurements of the frequency of neutron activity and T is the sample interval between the two frequency measurements. The resulting rate has units of decades per sample interval.
Instruments which measure neutron activity up to a few million pulses per second are commonly referred to as source range instruments. Such source range instruments, which are typically designed to cover a range of neutron activity from a few pulses per second to millions of pulses per second must meet specified response time criteria as well as specified accuracy and stability of measurement with respect to the measurement of the rate of change of frequency of neutron activity. To meet accuracy and stability requirements, the instrument must use a sufficiently long sampling interval so that variations in the reading due to the random nature of neutron activity are minimized. To meet response time requirements, the instrument must provide an accurate and stable reading in a timely fashion. The response time requirements generally vary over the operating range of the instrument from ten's of seconds at the low end to one second or less in the upper operating range. Different response times are also generally specified based on the type of input presented to the instrument. For example, response time requirements may be separately specified for exponentially increasing inputs and step change inputs. Therefore, the instrument may be required to distinguish between exponential changes in inputs and step changes in inputs. This feature is needed so that a small step change in input does not produce an indication of an abnormally high rate of change that may needlessly cause a trip in the reactor.
If a source range instrument continuously monitors neutron activity and stores the received number of counts for successive 100 ma intervals as count values X.sub.1, X.sub.2, . . . X.sub.16,640, where X.sub.1 represents the number of counts received during the most recent 100 ma sample interval and X.sub.16,640 represents the oldest sample, then an estimate of the mean value of frequency, or level L, is calculated from the equation: EQU L=10(X.sub.1 +. . . +X.sub.N)/N
where L has units of counts per second. The value of N is chosen to meet the specific accuracy, response time and statistical stability requirements of the source range instrument. In previous instruments, the exponential rate, R, was typically calculated from two successive values of L. For example, if: EQU L.sub.1 =10(X.sub.1 +. . . +X.sub.N)/N EQU and EQU L.sub.2 =10(X.sub.2 +. . . +X.sub.M+1)/M
that is, L.sub.1 is the most recent calculation of level and L.sub.2 is the next most recent calculation of level, then a common method of calculating the exponential rate, R, is to use the equation: EQU R=600 log (L.sub.1 /L.sub.2)
where R has units of decades per minute.
This method can give acceptable results when N equals M, but this method is unsuitable where the number of samples used in the level calculation is dynamically changing to meet the various response time and accuracy requirements of the instrument. During exponential increases in the level, while N is changing, the consecutive sample periods in which N and M are not equal will cause the above calculation of rate to substantially overshoot the true value. This problem can be overcome by requiring that N equal M at all times for the purposes of the rate calculation. However, this method has additional problems. Since many terms used in the calculation of L.sub.1 are common to the calculation of L.sub.2, the two values are not statistically independent samples. This maximum overlap in terms causes the statistical fluctuations in the rate calculation to be considerably larger than if the calculation was done with statistically independent samples of the same number of terms. Furthermore, the number of terms used to provide the best estimate of level is not necessarily the optimum number used for the rate calculation.
It is therefore desired to provide an improved method of calculating the rate of change of frequency of random events which reduces statistical fluctuations in the calculated rate and readily distinguish between exponential changes in the inputs and step changes in the inputs.